It is well known with turning and drilling tools employing metal cutting inserts that the quality and precision of finish is a function of the tool geometry and machining conditions and, thereby the tool output. Thus, it is known that the higher the tool output, the lower the quality and precision of the finish. Thus, the cut surface tends to image to a greater or lesser degree the shape of the cutting edge of the tool insert or tip, this surface bearing a series of consecutive grooves. It is known to represent the quality of surface finish in terms of the mean depth h of these surface grooves and, as a first approximation, this mean surface depth R.sub.t can be given by the relationship ##EQU1## where f is the feed of the cutting tool and r is the nose radius of the insert. As used in the present application, the term "feed" denotes the traverse of the cutting tool with respect to the work piece in the direction of the axis of rotation of the work piece per unit rotation of the work piece.
From this relationship, it can be readily seen that h increases (and therefore the surface finish improves) with decreasing feed values and/or increasing nose radii.
It is, however, also well known that another factor which influences surface finish is the vibration induced in the tool by the cutting process. Thus, the surface finish is deleteriously affected by any increase in the vibration frequency and/or the amplitude of the vibrations. In this connection, it can be shown that the frequency and amplitude of the vibrations is directly related to the nature of the chip flow, in particular to the frequency of breakage of the chips produced in the cutting operation. Because an increased frequency of chip breakage necessarily involves the production of shorter chips, the vibration frequency increases with the reduction in the length of the chips.
At the same time, it can be shown that the amplitude of the vibrations is mainly related to the cutting forces which are generated during the cutting operations, these cutting forces tending to increase with increasing depth of cut a.sub.p. On the other hand, it is known that with relatively low depths of cut such as those which occur during finishing operations, and especially with insert noses having a relatively large radii r, that the frequency of vibrations induced in the tool (F.sub.r) tends to increase. Similarly, it is known that with tools where the angle of inclination of the cutting edge (.theta.) is relatively low, there is also a corresponding increase in vibrational frequency F.sub.r.
It will therefore be seen that the factors affecting the surface finish of the workpiece are numerous and the variation of one factor so as to improve the surface finish often carries with it a variation of another factor which tends to affect unfavorably the quality of surface finish.